Solved Examples of Impulse Approximation: Step-by-Step Solutions

📚 Quick Study Guide

• ⏱️ Impulse Approximation is used when a large force acts for a short time.
• ✍️ We approximate the force as an impulse, ignoring the details of how the force changes over time.
• 📐 The impulse, $J$, is defined as the change in momentum: $J = \Delta p = m\Delta v$.
• 💡 If the force is not constant, $J = \int F dt$, which is approximated as $F_{avg}\Delta t$.
• 🍎 Common applications include collisions, explosions, and impacts.
• ⚠️ The approximation is valid when the duration of the impact is very small compared to other time scales in the problem.
• 🔢 Remember to consider the direction of the impulse, as it is a vector quantity.

🧪 Practice Quiz

1. A baseball of mass 0.15 kg is struck by a bat. Its velocity changes from -20 m/s to +30 m/s. What is the magnitude of the impulse delivered to the ball?
   1. 7.5 Ns
   2. 4.5 Ns
   3. 1.5 Ns
   4. 3.0 Ns
2. A car crashes into a wall. The force exerted on the car during the impact is shown to be approximately constant at 10,000 N for a duration of 0.1 seconds. What is the impulse experienced by the car?
   1. 100 Ns
   2. 1,000 Ns
   3. 10,000 Ns
   4. 100,000 Ns
3. A 0.5 kg ball is dropped from a height and hits the ground with a velocity of 5 m/s. It rebounds with a velocity of 3 m/s. What is the magnitude of the impulse imparted to the ball by the ground?
   1. 1 Ns
   2. 4 Ns
   3. 2 Ns
   4. 0 Ns
4. A soccer ball is kicked, and the kicker's foot is in contact with the ball for 0.02 seconds. If the average force exerted on the ball is 500 N, what is the impulse imparted to the ball?
   1. 25 Ns
   2. 10 Ns
   3. 5 Ns
   4. 1 Ns
5. A hockey puck of mass 0.1 kg moving at 10 m/s is stopped by a player's stick in 0.05 seconds. Assuming a constant force, what is the magnitude of the force exerted by the stick on the puck?
   1. 20 N
   2. 10 N
   3. 40 N
   4. 5 N
6. A rocket ejects 10 kg of exhaust gas at a velocity of 2000 m/s in 1 second. What is the magnitude of the thrust force on the rocket?
   1. 2000 N
   2. 20,000 N
   3. 200 N
   4. 200,000 N
7. A bullet of mass 0.01 kg strikes a block of wood with a velocity of 500 m/s and comes to rest inside the block. If the stopping time is approximately 0.001 seconds, what is the average force exerted on the bullet by the wood?
   1. 500 N
   2. 5,000 N
   3. 50,000 N
   4. 5 N